What is 10 Choose 3? — C(10, 3) Combinations
There are 120 possible combinations when choosing 3 items from 10 (nCr = 120), and 720 permutations (nPr = 720).
Exact Answer
C(10, 3) = 120
Combinations C(n,r)
120
Permutations P(n,r)
720
n! (10!)
3,628,800
r! (3!)
6
Step-by-Step Solution: C(10, 3) = 120
Step 1
Use the Combinations Formula nCr = n! / (r! × (n − r)!)
Substitute n = 10 and r = 3: 10! = 3,628,800, (10−3)! = 5,040, and 3! = 6.
C(10, 3) = 120
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Combinations C(n,r) | 120 |
| Permutations P(n,r) | 720 |
| n! (10!) | 3,628,800 |
| r! (3!) | 6 |
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Frequently Asked Questions
What is the difference between C(10,3) and P(10,3)?
Combinations C(10,3) = 120 (order does not matter), whereas Permutations P(10,3) = 720 (order matters).